3 problems

Let $f_n$ be the number of $2\times n$ matrices containing a $1$ in the top left entry, with integer entries such that adjacent entries differ by at most $1$. Let $a_n$ be the numb…

Let $G$ be a convex benzenoid, let $\operatorname{\mathfrak{a}}(G,H)$ be its altan for an attachment set $H$, and let $\eta$ and $\eta(\operatorname{\mathfrak{a}})$ denote the null…

Let $h\geq 0$, and let $F(h,k)$ denote the number of benzenoids on $h$ hexagons having convexity deficit equal to $k$. Let $\operatorname{mcd}(h)$ be the maximum convexity deficit…